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Identifying Elementary Iterated Systems through Algorithmic Inference: the Cantor Set Example
bruno apolloni and simone bassis
Chaos, Solitons and Fractals
Volume 30,
,
2006.
AbstractWe come back to the old problem of fractal identification
within the new framework of Algorithmic Inference. The key points are: i) to
identify sufficient statistics to be put in connection with the unknown values
of the fractal parameters, and ii) to manage the timing of the iterated process
through spatial statistics. We fill these tasks successfully with the Cantor Sets. We are
able to compute confidence intervals for both the scaling parameter $\vartheta$ and the
iteration number $n$ at which we are observing a set. We both check ùly the
coverage of these intervals and delineate a general strategy for affording more
complex iterated systems. [Edit]
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